1. Field of the Invention
This invention relates to a balance and an elastic force reducing dynamometer. More particularly, this invention relates to a balance and elastic force reducing dynamometer having primary and secondary elastic force transfer springs connected in parallel.
2. Background of the Invention
Balances and dynamometers having primary and secondary elastic force transfer springs are described, for example, in European Patents B1 16,238 and B1 25,807 and West German Patent DE Gbm. G 86 33 612.6. In such devices, the total force being measured by the device is distributed onto two springs connected in parallel. The parallel connected springs include a first or primary spring and a secondary spring. The primary spring diverts the major portion of an input force F.sub.i directly to the frame of the device and to a second spring. A force sensor for converting the measured force into an electrical value, is installed in series with the second spring. As most force sensors are characterized by a specific elastic compliance, the force sensor may be viewed as yet another spring. Thus, the secondary spring is comprised of the second spring together with the serially connected force sensor.
In the simplest configuration, the primary and secondary springs are similarly connected such that the application of an input force F.sub.i produces the same deflection in both springs. In this case, the input force would be distributed between the two springs according to their respective degree of rigidity. Accordingly, the reduction ratio U may be calculated according to the following formula: ##EQU1## where: F.sub.i is the input force;
F.sub.o represents the portion of F.sub.i acting on the force sensor; PA1 k.sub.1 is the force constant or rigidity of the primary spring; PA1 k.sub.2 is the force constant or rigidity of the secondary spring including the force sensor; PA1 c.sub.1 is the inverse of k.sub.1 or the compliance of the primary spring; and PA1 c.sub.2 is the inverse of k.sub.2 or the compliance of the secondary spring including the force sensor. PA1 F is the force being applied; and PA1 c is a constant.
If the compliance of the second spring is designated as c.sub.21 and the compliance of the force sensor as c.sub.22, then U may be expressed as: ##EQU2##
In other configurations, the primary and secondary springs are separately connected but are still coupled together such that the deflection of one spring is proportional to that of the other. If all compliances and forces on the common connections are reduced mathematically, equations (1) and (2) are equally applicable.
Hooke's law provides that the force applied to an elastic body is proportional to the extension or compression undergone by that body. In accordance with Hooke's law, the compliances contained in equations (1) and (2) are constants so long as their temperature dependence is not taken into consideration. This relationship may be expressed in mathematical terms as follows: ##EQU3## where: L is the extension or deflection of the elastic body;
It should be noted, however, that Hooke's law is merely a good approximation and not a positive relationship. Several deviations from this approximation are known in practice. For example, the delayed elasticity of the spring material leads to a time dependent, delayed deflection of the spring body fabricated from such material. This phenomena is generally referred to as "creep" and has been well documented in the literature. See, for example, A. S. Nowick and B. S. Berry: Anelastic Relaxation in Crystalline Solids, Academic Press, New York and London, 1972. The term "relative creep" has been used to designate the ratio between the time dependent and time independent components of a compliance. The value of relative creep varies with the nature of the material and, for each material, with the temperature and type of stress involved, e.g. compressive stress vs. shear stress. Values for relative creep above 1/1000 have been measured in the 0.degree. C. to 40.degree. C. temperature range.
Because the phenomena of creep has an adverse affect on the precision of balances and dynamometers, various solutions have been proposed for compensating and/or reducing the influence of creep on weight measurements. For example, in Swiss Patent A5 656,225, a solution was proposed that required all deflection points to be made of the same material. It was also required that the change in flexural stress be equal everywhere. Because of these requirements, the proposed solution was less than satisfactory. First, a measuring system is typically made using a material different from the material used for the deflecting springs. Moreover, the proposed solution is based on the assumption that creep proceeds non-linearly with flexural stress, an assumption that is not necessarily correct.
It is an object of this invention to provide an elastic force reducing balance and dynamometer having primary and secondary elastic force transfer springs connected in parallel.
It is another object of this invention to provide an elastic force reducing balance and dynamometer which compensates for the relative creep of the primary and secondary springs.